SAT Math Level 2 - ALGEBRA Flashcards
Difference of Two Squares: X^2 - Y^2 =
( x + y )( x - y )
Graph of Quadratic Function: f(x) =
ax^2 + bx + c
For the graph of quadratic function, the x-value of the vertex is
x value = -b/2a
If y = a(x-h)^2 + k, then the vertex of the parabola is
(h,k)
If y = ax^2 + bx + c, the sum of the two roots are
-b/a
If y = ax^2 + bx + c, the product of the two roots are
c/a
Is 1 a prime number?
NO!
1 foot is equal to _____ inches?
12 inches
Polynomial
A finite sum of positive integer powers of a variable, often x
Degrees in a polynomial
The degree is the highest power of x in the polynomial. etc. 5x^6 + 3x^3 - 5x –> the degree is 6
Leading coefficient
The coefficient of the highest power of x
etc. 21x^4 + 10x^6 - 3 –> the leading coefficient is 10
Properties of polynomials
- every polynomial is continuous: they have no gaps or holes
- they are smooth everywhere: polynomial graphs don’t have sharp points or cusps
- a degree n polynomial has at most n real roots: it can cross the x-axis in at most n different places
- A degree n polynomial graph has at most (n-1) “bumps” on it (max min point)
Not polynomials
1/x, x^2 + square root x and sinx
Four quadrants in a plane
- 1st quadrant - x and y positive (upper right)
- 2nd quadrant - x negative and y positive (upper left)
- 3rd quadrant - x and y negative (lower left)
- 4th quadrant - x positive and y negative (lower right)
Even degree polynomials
Positive leading coefficient
- graph moves from quadrant 2 to quadrant 1
Negative leading coefficient
- graph moves from quadrant 3 to quadrant 4
Odd degree polynomials
Positive leading coefficient
- graph moves from quadrant 3 to quadrant 1
Negative leading coefficient
- graph moves from quadrant 2 to quadrant 4
loga(a) =
1
loga(1) =
0
Change of base formula (Logs)
loga(X) = logb(X) / logb(A)
Absolute value
The number “made positive”
etc. | 6 | = 6 , | -7 | = 7
| x | ^2 = | x^2 | = x^2
| x | = | -x |
If y varies directly to x then
y = kx k = constant of proportionality
If y varies indirectly to x then
y = k/x k = constant of proportionality
n! =
n x (n - 1) x (n - 2) x ... x 3 x 2 x 1 etc. 6! = 6 x 5 x 4 x 3 x 2 x 1
1! =
1
0! =
1
Vertex
Lowest or Highest point on a parabola
